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Mathematics Unit Outcomes and Assessment Standards Progression Table National 4 and 5 Access 3 National 4 Expressions and Formulae 4 National 5 Expressions and Formulae 5 1 1 1.1 1.2 1.3 1.4 1.5 1.6 2 2.1 2.2 2.3 2.4 2.5 2.6 3 3.1 3.2 3.3 3.4 3.5 4 Use algebraic skills linked to straightforward expressions and formulae by: Using the distributive law in an expression with a numerical common factor to produce a sum of terms Factorising a sum of terms with a numerical common factor Simplifying an expression which has more than one variable Evaluating an expression or a formulae which has more than one variable Extending a straightforward number or diagrammatic pattern Determining a formula from information or a diagrammatic pattern Use geometric skills linked to straightforward expressions and formulae by: Calculating the circumference and area of a circle Calculating the area of a parallelogram, kite, trapezium Investigating the surface of a prism Calculating the volume of a prism Investigating the gradient of a straight line Using rotational symmetry Use statistical skills linked to straightforward expressions and formulae by: Constructing a frequency table Determining statistics of a data set Interpreting calculated statistics Representing data in a diagram Using probability Use mathematical reasoning skills linked to straightforward expressions and formulae by: 4.1 Interpreting a situation where mathematics can be used 4.2 Identifying a valid strategy 4.3 Explaining a solution and relating it to context 1.1 1.2 1.3 2 2.1 2.2 2.3 2.4 2.5 2.6 3 3.1 3.2 3.3 4 4.3 4.4 4.3 Use numerical skills linked to expressions and formulae by: Working with surds Simplifying expressions using the laws of indices Rounding to a given number of significant figures Use algebraic skills linked to expressions and formulae by: Working with algebraic expressions involving brackets Factorising an algebraic expression Completing the square in a quadratic expression with unitary x2 coefficient Reducing an algebraic fraction to its simplest form Applying the four operations to algebraic fractions Working with number sequences Use geometric skills linked to expressions and formulae by: Determining the gradient of a straight line, given two points Calculating the length of arc or the area of a sector of a circle Calculating the volume of a standard solid Use mathematical reasoning skills linked to expressions and formulae by: Interpreting a situation where mathematics can be used Identifying a valid strategy Explaining a solution and relating it to context Relationships 4 Relationships 5 1 1 1.1 1.2 1.3 2 2.1 2.2 2.3 3 3.1 3.2 Use algebraic skills related to straightforward relationships by: Drawing and recognising a graph of a linear equation Solving linear equations Changing the subject of a formula Use geometric skills related to straightforward relationships by: Using Pythagoras’ theorem Using a scale factor to enlarge or reduce a shape Using properties of shapes and parallel lines Use trigonometric skills related to straightforward relationships by: Calculating a side in a right-angled triangle Calculating an angle in a right-angled triangle 1.1 1.2 1.3 1.4 2 2.1 2.2 2.3 2.4 3 4 4.1 4.2 5 5.1 5.2 5.3 Use statistical skills related to straightforward relationships by: Constructing a scattergraph Drawing and applying a best-fitting straight line 3.1 3.2 3.3 Use mathematical reasoning skills linked to straightforward relationships by: Interpreting a situation where mathematics can be used Identifying a valid strategy Explaining a solution and relating it to context 4 4.1 4.2 Use algebraic skills linked to linear relationships by: Determining the equation of a straight line Working with linear equations and inequations Working with simultaneous equations Changing the subject of a formula Use algebraic skills linked to quadratic relationships by: Sketching a quadratic function Determining the equation of a quadratic function from its graph Identifying features of a quadratic function Working with quadratic equations Use geometric skills linked to relationships by: Applying the converse of Pythagoras Theorem Applying the properties of shapes Using similarity Use trigonometric skills linked to relationships by: Working with the graphs of trigonometric functions Working with trigonometric relationships in degrees Numeracy 3 Numeracy 4 Applications 5 1 1 Use numerical skills to solve given, straightforward reallife problems involving money/time/measurement by: 1 1.1 Selecting and using appropriate numerical notation and units 1.2 Selecting and carrying out calculations involving: whole numbers, fractions, decimals, percentages, ratio and proportion. Collectively these require evidence of all of the following: addition, subtraction, multiplication and division 1.1 1.2 1.3 1.4 1.5 2 2.1 Use numerical skills to solve given, simple reallife problems involving money/time/ measurement by: Selecting and using appropriate numerical notion and units Selecting and carrying out calculations involving: whole numbers, simple fractions, simple decimals and simple whole number percentages. Collectively these require evidence of all of the following: addition, subtraction, multiplication and division 1.1 1.2 1.3 Reading measurements using a straightforward scale on an instrument 1.4 Interpreting measurements and results of calculations to make decisions 1.5 Explaining decisions based on the results of measurements and calculations 3 2 Interpret graphical data and situations involving probability to solve given, straightforward real-life problems involving money/time/measurement by: 3.1 3.2 3.3 2.1 Extracting and interpreting data from at least two different straightforward graphical forms 4 2.2 Making and explaining decisions based on the interpretation of data from straightforward graphical forms 4.1 4.2 2.3 Making and explaining decisions based on probability Extracting and interpreting data from at least one simple graphical form 2.2 Making decisions based on interpretation of data from a simple graphical form 2.3 Making decisions based on probability 2.1 2.3 Interpreting measurements and the results of calculations Interpret graphical data and situations involving probability to solve given, simple real-life problems involving money/time/measurement by: 2 2.2 Reading measurements using a simple scale on an instrument Making decisions based on the results of measurements and calculations 1.3 5 Use trigonometric skills linked to applications by: Calculating the area of a triangle using trigonometry Using the sine and cosine rules to find a side or angle Using bearings with trigonometry Use geometric skills linked to applications by: Adding or subtracting two-dimensional vectors using directed line segments Interpreting three-dimensional coordinates or directed line segments which are given in diagrams Adding or subtracting two- or three- dimensional vectors using components Use numerical skills linked to applications by: Working with percentages Working with proportion Working with fractions Use statistical skills linked to applications by: Comparing data sets using statistics Forming a linear model from a given set of data Use mathematical reasoning skills linked to applications by: 5.1 Interpreting a situation where mathematics can be used 5.2 Identifying a valid strategy 5.3 Explaining a solution and relating it to context